Has 2 adjustable handles, fits a car seat, can be forward or rear facing, is lightweight, has a decent sized shopping basket, looks funky, is in a colour that is not gender specific and is easy to keep clean, folds up easily, has hard wheels, a freedom to explore harness and costs under £250?
Mamas and papas Pliko P3?? I've just got one cost £230. Its only rear facing as a pramette though. The pushchair costs £240, but if brought with the liner to turn it into a pramette and the changing bag you save £100 taking it down to £230. Car seat is an extra £110 though.
We went to a number of stores (John Lewis, Mothercare, Mamas & Papas), found a helpful assistant and went through our requirements with them (lightweight, suitable from birth, forward & rear facing, v high handles). They found a number of ones for us to choose from. You'll find that the forward & rear facing option really reduces your choice though, so have a think about how essential it is (we stuck with it, but our choices were tiny as a result). You can then check the choices against the mumsnet review section (and I've even been known to stop people in the street to get their verdict on their pram!). Good luck.
Maclaren Techno XLR if you can drop the forward facing bit? It has a viewing window so you can still see the baby clearly. Bit of a crap shopping basket mind-in fact not what you are asking for at all but I think they are the best from birth pushchair around and can take a car seat.
Mamas & Papas do a new version of the Pliko P3 called the Switch which now has a forward or rearfacing pushchair seat, unfortunately it is £322 on the M&P website (reduced from £350), however I think Peg Perego (who actually make the pushchairs for M&P) also sell it under their own branding for cheaper.
We have an ICandy cherry which does what you want, but you have to get the carrycot for 0-6 months which brings the price to £300. There have been some problems with the front wheels, and we have had ours replaced twice, but has been fine ever since as apparently they redesigned them. The colours are a bit limited, but both are unisex, we have the red/black and I quite like it. However it doesn't have 2 adjustable handles, and it folds in two pieces so no good for the bus and the harness is fixed, but there are D-rings so you could fit your own?
Mumsnet is a great resource - there is another thread where someone ordered the Switch from an italian website: here it is it's showing as 329 Euros, which is about £260, though the other thread mentioned £238 + £10 delivery. Seems like a good deal.
bebe confort loola - cant remember how much it was but think we got one in last years colours (red) and it was pretty cheap - car seat and carrycot thing sold separately but we didnt bother with the carrycot as the seat lay flat.
has all the other features you mention. adjustable handles not huge adjustment available but i'm 5ft 3 and dh is 6 ft 2 and we both used it quite happily.